Contrazione di SU(2) sul Gruppo di Heisenberg

In this thesis we want to analyze the irreducible unitary representations of SU(2) and those of the Heisenberg group. The infinite-dimensional (irreducible unitary) representations of the Heisenberg group will be shown to be limits of finite (irreducible unitary) representations of SU(2). In order to define the notion of representations convergence, we have to study the Lie group contraction, a modern mathematical technique which is able to establish a local identification between two continuous connected groups of the same dimension. We will see that the contraction of the two groups also induces the contraction of their respective Lie algebras, so we can deal with the Heisenberg Lie algebra as it was the limit case of the Lie algebra of SU(2).